few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Use random sampling to draw inferences about a population.

Use probability to evaluate outcomes of decisions.

Calculate expected values and use them to solve problems.

Understand independence and conditional probability and use them to interpret data.

Interpret linear models.

Draw informal comparative inferences about two populations.

Understand and evaluate random processes underlying statistical experiments.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Investigate patterns of association in bivariate data.

Summarize and describe distributions.

Summarize, represent, and interpret data on a single count or measurement variable.

Develop understanding of statistical variability.

Investigate chance processes and develop, use, and evaluate probability models.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
problem_activity: In Class Launch
Use after Unit 1, Lesson 15
Ask students to think about a question they are interested in that they would need to gather data in order to answer. They will choose one of these questions, find data relevant to it, and present their results with a data display or an infographic. Either show students examples of infographics or ask them to look up a few examples.
Students can be arranged in groups in advance, or they can choose groups based on the questions they are most interested in.
Teacher Instructions
Students may not be able to find the information they need to answer the question they were originally interested in. They can refine and change their question to align with the data available.
If students are not sure where to begin, it might be helpful for them to think about questions that compare two groups, since they have been doing a lot of work with comparing data sets using measures of center and variability, and this is the kind of data analysis they will be expected to do.
Student-Facing Statement
Choose a question that you think is interesting and that you do not know the answer to. You will gather data relevant to this question by either doing an experiment or researching available data, so choose a reasonable question.
Write your question.
What do you predict you will learn from the data?
Next, gather your data. Then choose one of these options for displaying your data and answer the questions about it.
Option 1: Create a display that shows the distribution of the data. Include both measures of center and measures of variability.
Why is the data display you selected the best way to summarize your data?
Is any of the data surprising?
Are there any outliers? If so, tell their story. If not, why do you think not?
Describe the shape of the distribution.
Option 2: Use an infographic to summarize what you found.
Why is an infographic the best way to summarize your data?
Is any of the data surprising?
What story does your infographic tell?
Now that you have seen some data, is there another, related question you would like to study or some additional data you would like to collect?
Teacher Instructions
Give students a source of data and let them explore it for a few minutes and share observations in pairs or groups before they begin working on the task statement. This task can be further scaffolded by giving students data that is easier to work with.
If students are not sure where to begin, it might be helpful for them to think about questions that compare two groups, since they have been doing a lot of work with comparing data sets using measures of center and variability, and this is the kind of data analysis they will be expected to do.
Student-Facing Statement
What are some questions that you might be able to answer with the given data?
Choose one of your questions to try to answer. What do you predict the data will tell you?
Look for data that’s relevant to your question. You might have to change your question a little if you can’t find the data you need to answer the original question. When you have an answer, choose a way of displaying the data that will help other people understand what you learned.
Option 1: Create a display that shows the distribution of the data. Include both measures of center and measures of variability.
Why is the data display you selected the best way to summarize your data?
Is any of the data surprising?
Are there any outliers? If so, tell their story. If not, why do you think not?
Describe the shape of the distribution.
Option 2: Use an infographic to summarize what you found.
Why is an infographic the best way to summarize your data?
Is any of the data surprising?
What story does your infographic tell?
Now that you have seen some data, is there another, related question you would like to study or some additional data you would like to collect?


correct_option_index: 11